DPOTRI(3)

💅 DPOTRI(3) — the girlies' guide to inverting a Cholesky factor ✨

okay so real talk, bestie: this page lives in the Library Functions Manual, and its whole government name is /home/abui...RC/dpotri.f(3). Say it with me now. Slay. 🎀

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dpotri.f

like yes, that's the whole name, she's dramatic, we love her for it 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine DPOTRI (uplo, n, a, lda, info) — this is the moment, this is the girl, DPOTRI

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🦋 Function/Subroutine Documentation 🦋

subroutine DPOTRI (character uplo, integer n, double precision, dimension(
    lda, * ) a, integer lda, integer info)

DPOTRI — the icon herself 👑

🫶 Purpose:

!>
!> DPOTRI computes the inverse of a real symmetric positive definite
!> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
!> computed by DPOTRF.
!>

so basically: you already did your Cholesky factorization with DPOTRF (that's the hard part, she did all the work), and now DPOTRI takes that factor and flips the whole thing into the actual inverse of A. no cap, it's giving "cleanup crew" energy 💖

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🔥 Parameters 🔥

• UPLO — like, UPLO is CHARACTER*1, and she's the vibe check for where your triangle lives:

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

• N — N is INTEGER, the order of the matrix A. and the rule is N >= 0. periodt ✨

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

• A — A is DOUBLE PRECISION array, dimension (LDA,N). okay so on entry, she's holding the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPOTRF. on exit?? glow-up 💅 she now holds the upper or lower triangle of the (symmetric) inverse of A, overwriting the input factor U or L. literally main character energy, out with the old in with the new.

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the triangular factor U or L from the Cholesky
!>          factorization A = U**T*U or A = L*L**T, as computed by
!>          DPOTRF.
!>          On exit, the upper or lower triangle of the (symmetric)
!>          inverse of A, overwriting the input factor U or L.
!>

• LDA — LDA is INTEGER, the leading dimension of the array A. and bestie, LDA >= max(1,N). the max is not optional, don't test her 🙈

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

• INFO — INFO is INTEGER, and honestly she's the group chat read receipt:

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, the (i,i) element of the factor U or L is
!>                zero, and the inverse could not be computed.
!>

so = 0 means successful exit (ate, no crumbs 💀✨), < 0 means if INFO = -i then the i-th argument had an illegal value (someone showed up wrong 😭), and > 0 means if INFO = i then the (i,i) element of the factor U or L is zero, and the inverse could not be computed. like she tried. she couldn't. respect the process 🫶

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

the whole friend group collaborated, we stan a collective 💜

Definition at line 94 of file dpotri.f.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. (yes she was built by a robot, she still has feelings ⭐)

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so that's the whole thing, bestie — go invert something symmetric and positive definite, you're gonna do great 🌈

LAPACK · Version 3.12.0 · from /home/abui...RC/dpotri.f(3) — mwah, ilysm, now go run your Fortran 💖🎀🦋